new fatou.gp program - Printable Version +- Tetration Forum (https://math.eretrandre.org/tetrationforum) +-- Forum: Tetration and Related Topics (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1) +--- Forum: Computation (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=8) +--- Thread: new fatou.gp program (/showthread.php?tid=1017) Pages: 1 2 3 4 RE: new fatou.gp program - JmsNxn - 07/07/2022 Hmm, Okay That's something I've never seen before. You are right, Catullus, I've made a mistake somewhere in my observations. From here, I don't have an answer to your question. I am not familiar enough with the fatou.gp program. I thought it'd run the Schroder for $$i$$, didn't realize it ran the kneser algorithm. I guess the best statement that I have is that for $$1 < b < \eta$$ Sheldon's algorithm runs a kneser algorithm which roughly approximates the Schroder iteration. But for complex values it runs the Kneser iteration, as an analytic continuation. I'm still wary though of this solution. I apologize, my mistake. RE: new fatou.gp program - Catullus - 07/09/2022 Then what was up with the spikes in the imaginary part with one precision, and then straight line at zero at a higher precision? How do I use fatou.gp to show the non real valuedness of the analytic continuation of the Kneser method, with base the pith root of pi in a way that is not spikey? RE: new fatou.gp program - JmsNxn - 07/10/2022 (07/09/2022, 06:55 AM)Catullus Wrote: Then what was up with the spikes in the imaginary part with one precision, and then straight line at zero at a higher precision? How do I use fatou.gp to show the non real valuedness of the analytic continuation of the Kneser method, with base the pith root of pi in a way that is not spikey? You never use numerical approximation as a proof of anything. So, you can't. But the spikes are just noise in the program... nothing you can do about that--except write your own program that tries to reduce noise. RE: new fatou.gp program - Catullus - 07/10/2022 (07/10/2022, 01:51 AM)JmsNxn Wrote: (07/09/2022, 06:55 AM)Catullus Wrote: Then what was up with the spikes in the imaginary part with one precision, and then straight line at zero at a higher precision? How do I use fatou.gp to show the non real valuedness of the analytic continuation of the Kneser method, with base the pith root of pi in a way that is not spikey? You never use numerical approximation as a proof of anything. So, you can't. But the spikes are just noise in the program... nothing you can do about that--except write your own program that tries to reduce noise.What about using tetcomplex.gp?